Tough DS

Expert replies

rainmaker: Senior | Next Rank: 100 Posts; Posts: 63; Joined: Mon Jul 20, 2009 11:48 am; GMAT Score:730

by rainmaker » Sat Aug 22, 2009 6:51 pm

Please explain your answer:

In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) sqrt(a^2) + sqrt(b^2) = sqrt(c^2) + sqrt(d^2)

where ^ means "raised to the power of"

Like this post

Source: Beat The GMAT — Data Sufficiency | Sat Aug 22, 2009 6:51 pm

iamjakekim: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Sun Jun 21, 2009 12:09 pm; Thanked: 1 times; GMAT Score:700

by iamjakekim » Sat Aug 22, 2009 10:08 pm

I think it is D

STM1.

if you cross multiply, you get b/a = d/c

STM2.

We need to know whether distance is equal.

For example, (1,4) and (4,1) are equal distance.
(-1,5) and (1,-5) are equal distance.!!

DDDDDD

Like this post

shanrizvi: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Tue Aug 11, 2009 2:30 am; Thanked: 2 times; GMAT Score:720

by shanrizvi » Sun Aug 23, 2009 1:48 pm

In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

Statement 1: a/b = c/d

If (a,b) is (2,4) and (c,d) is (-2,-4), a/b = c/d and the points are equidistant. However, if (a,b) is (2,4) and (c,d) is (4,8), a/b = c/d but the points are not equidistant. Hence, the statement is insufficient.

Statement 2: sqrt(a^2) + sqrt(b^2) = sqrt(c^2) + sqrt(d^2)

For any point (x,y), the distant from the origin is sqrt(x^2+y^2). As this is NOT equal to sqrt(a^2) + sqrt(b^2), I say this statement is insufficient.

To prove this, plot any point (x,y) on the graph and consider the triangle bound by lines X=x, Y=y and the line from origin to (x,y). The distance to origin is the hypotenuse of the triangle with the other 2 sides of lengths x and y.

Like this post

pradeepsarathy: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Wed Jul 09, 2008 7:12 amFollowed by: 1 member; Location: Secaucus, New Jersey; Thanked: 3 times; GMAT Score:700

by pradeepsarathy » Tue Aug 25, 2009 7:07 pm

IMO C

Stmt 1 - a/b = c/d

Case 1 - a = 1, b = 1, c = 2, d = 2
while a/b = c/d, the points are not equidistant from origin

Case 2 - a = -1, b = -1, c = 1, d = 1
a/b = c/d and also the points are equidistant from origin,
Hence stmt 1 alone is insufficient.
Eliminate answer choices A and D

Stmt 2 - sqrt(a^2) + sqrt(b^2) = sqrt(c^2) +sqrt(d^2)

Case 1 - a = 1, b = 2, c = 0, d = 3
while the points satisfy stmt 2, they are not equidistant from origin.

Case 2 - a = 1, b = 2, c = -1, d = -2
the points both satisfy the stmt 2 and also are equidistant from origin.

Hence stmt 2 alone is insufficient

Eliminate choice B.

Combining both stmt 1 and stmt 2 -
we see that the points have to be symmetrically oppisite to each other, and hence they will be equidistant from the origin as well.

Hence both stmts are sufficient.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review